Ph.D Student | Kavaler Itay |
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Subject | On Comparison of Experts |

Department | Department of Industrial Engineering and Management |

Supervisor | PROF. Rann Smorodinsky |

The thesis addresses two areas of research. Multi - expert testing on the one hand, a topic that studies whether decision makers can reasonably learn to make comparisons while facing many experts’ advice, and sequential social learning on the other. The latter refers to situations in which a sequence of privately informed individuals make a decision while observing decisions made by predecessors.

Multi - expert testing? In various situations, decision makers face experts that may provide conflicting advice. This advice may be in the form of probabilistic forecasts over critical future events. We consider a setting where the two forecasters provide their advice repeatedly and ask whether the decision maker can learn to compare and (weakly) rank the two forecasters based on past performance. We take an axiomatic approach and propose three natural axioms that a comparison test should comply with. We show that these determine the test in an essentially unique way.

We explore two modelling approaches resolving. In the first approach we consider an infinite horizon setting where decisions are made at the end of all times. We show that the resulting test is a function of the derivative of the induced pair of measures at the realized outcomes. This is discussed in detail in chapter 2 which is based on Kavaler and Smorodinsky (2019a). In the second approach, comparisons are made at each stage. Perhaps, not surprisingly, the test is closely related to the likelihood ratio of the two forecasts over the realized sequence of events. More surprisingly, this test is essentially unique. Furthermore, using results on the rate of convergence of supermartingales, we show that whenever the two experts‘ advice are sufficiently distinct, the proposed test will detect the informed expert in any desired degree of precision in some fixed finite time. This is discussed in detail in chapter 3 which is based on Kavaler and Smorodinsky (2019b).

Sequential social learning?In the classical herding model, asymptotic learning refers to situations where individuals eventually take the correct action regardless of their private information. Classical results identify classes of information structures for which such learning occurs. Recent papers have argued that typically, even when asymptotic learning occurs, it takes a very long time. In this research related questions are referred. The research studies whether there is a natural family of information structures for which the time it takes until individuals learn is uniformly bounded from above. Indeed, we propose a simple biparametric criterion that defines the information structure, and on top of that compute the time by which individuals learn (with high probability) for any pair of parameters. Namely, we identify a family of information structures where individuals learn uniformly fast.

The underlying technical tool we deploy is a uniform convergence result on a newly introduced class of ‘weakly active’ supermartingales. This result extends an earlier result of Fudenberg and Levine (1992) on active supermartingales.